Question

Dinosaur fossils are often dated by using an element other than carbon, like potassium-40, that has a longer half life (in this case, approximately 1.25 billion years). suppose the minimum detectable amount is 0.1% and a dinosaur is dated with 40k to be 67 million years old. what is the maximum age of a fossil that we could date using 40k? (round your answer to one decimal place.)

Answer 1

The maximum age of a fossil that could be dated using 40K is approximately 5.36 billion years.

Step-by-step explanation:

Potassium-40 (40K) has a half-life of 1.25 billion years.

The minimum detectable amount for dating using 40K is 0.1%. If a dinosaur is dated using 40K to be 67 million years old, we can calculate the maximum age of a fossil that could be dated using 40K.

To find the maximum age, we can set up a proportion using the half-life of 40K:

(67 million years) / (1.25 billion years) = (x years) / (100%)

Solving for x, we get:

x = (67 million years) * (100%) / (1.25 billion years)

Calculating this, we find that the maximum age of a fossil that could be dated using 40K is approximately 5.36 billion years.

Answer 2

The amount of substance left of a radioactive element of half life,
`t_{(1)/(2)}` after a time, t, is given by:


`N(t)=N_0\left( (1)/(2) \right)^ \frac{t}{t_{ (1)/(2) }}`

Given that potassium-40 has a half life of approximately 1.25 billion years.

The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:


`0.1=100\left( (1)/(2) \right)^ (t)/(1.25)} \\ \\ \Rightarrow\left( (1)/(2) \right)^ (t)/(1.25)}=0.001 \\ \\ \Rightarrow(t)/(1.25)\ln\left( (1)/(2) \right)=\ln(0.001) \\ \\ \Rightarrow (t)/(1.25)= (\ln(0.001))/(\ln\left( (1)/(2) \right)) =9.966 \\ \\ t=9.966(1.25)=12.5`

Therefore, the maximum age of a fossil that we could date using 40k is 12.5 billion years.